带一阶导数项多滞量二阶中立型方程解的振动的充要条件

考虑中立型方程其中p_i,r_j(i∈I,j∈J)为任意实常数,q_k,τ_i(k∈K,i∈J)为正常数,而ρ_j,σ_k(j∈J,k∈K)是非负常数。则方程(*)所有解振动的充要条件是它的特征方程无实根。

Necessary and Sufficient Conditions for Oscillations of Second-order Neutral Equations with First-order Derivative Terms and Several Delays

Consider the neutral equations where p_i,r_j for i∈I, j∈J are arbitrary real constants, q_k for k E K, r, for i ∈ I are positive constants while ρ_j, σ_k for j∈J and k∈K are nonnegative constants. Then a necessary and sufficient condition for oscillations of all solutions of Eqns (*) is that its Characteristic equations has no real roots.The equations disscused in 1] and 2] (n=2) is a special case of Eqns (*). We have proved that as for Eqns ( * ) the Theorems in 1] and 2] (n=2) is also true.